Set Theory Test...

If two sets $$A$$ and $$B$$ are having $$99$$ elements in common, then the number of ordered pairs common to each of the sets $$AxB$$ and $$BxA$$ are

If $$X =\{1,2,3,4,5,6,7,8,9, 10\}$$ is the universal set and$$ A= \{1, 2, 3,4\}, B= \{2,4,6,8\}, C= \{3,4,5,6\}$$  verify the following.
(a) $$A \cup (B\cup C) = (A \cup B) \cup C$$
(b)$$A \cap (B\cup C) = (A \cap B) \cup (A \cap C)$$
(c) $$(A')' =A$$

$$S_1:(p\Rightarrow q) V ( q \Rightarrow p )$$ is a tautology.
$$S_2: ((p\Rightarrow q) V ( q \Rightarrow p))$$ is a fallacy

$$If\,A = \left\{ {\left( {x,y} \right)\,\left| {{x^2} + {y^2} \le \left. 4 \right\}\,and} \right.} \right.$$
$$B = \left\{ {\left( {x,y} \right)\,\left| {{{(x - 3)}^2} + {y^2}} \right. \le \left. 4 \right\}} \right.\,and\,the$$
$$po{\mathop{\rm int}} \,P\left( {a,\frac{1}{2}} \right)\,belongs\,to\,the\,set\,B - A$$ then the set of possible real values of $$a$$ is

In a selection process, a hundred candidate participate in Group Discussion sessions (GD) and Personal Interview (PI). The possibilities of a candidate's good performance in GD and in PI are independent of each other. It was found that $$20$$ candidates were good in GD and $$30$$ were good in PI. The number of candidates good in both GD and PI is expected to be about:

If $$A \subset B$$, then

The set of all $$x$$ for which $$1 + \log x < x$$ is

$$s = \{ x \in N:2 + {\log _2}\sqrt {x + 1}  > 1 - {\log _{1/2}}\sqrt {4 - {x^2}} \} $$ , then

If $$\alpha,\xi,\eta$$ are non-empty sets then:

For any two sets A and B, A' - B' is equal to